3. PLANEACIÓN AGREGADA
3.5. MRP (MATERIALS REQUERIMENT PLANNING)
3.5.3 Técnicas de dimensionado del lote
Keep the Plant
Open Close the Plant Sales (5,000 units × $40 per unit). . $ 200,000 $ 0 Variable expenses
(5,000 units × $24 per unit)... 120,000 0 Contribution margin... 80,000 0 Fixed expenses:
Fixed manufacturing overhead cost:
$400,000 × 3/12... 100,000
$400,000 × 3/12 × 60%... 60,000 Fixed selling expense:
$360,000 × 3/12... 90,000
$360,000 × 3/12 × 2/3... 60,000 Total fixed expenses... 190,000 120,000 Net operating income (loss)... $(110,000) $(120,000
) 4. The relevant cost is $1.70 per unit, which is the variable selling
expense per Zet. Since the blemished units have already been produced, all production costs (including the variable
production costs) are sunk. The fixed selling expenses are not relevant since they will remain the same regardless of whether or not the blemished units are sold. The variable selling
expense may or may not be relevant—depending on how the blemished units are sold. For example, the units may be sold through a liquidator without incurring the normal variable selling expense.
To be acceptable, the outside manufacturer’s quotation must be less than $26.82 per unit.
Problem 13-23 (60 minutes)
1. The $2.00 per unit general overhead cost is not relevant to the decision, since the total general company overhead cost will be the same regardless of whether the company decides to make or buy the subassemblies. Also, the depreciation on the old equipment is not a relevant cost since it represents a sunk cost and the old equipment is worn out and must be replaced. The cost of supervision is relevant since this cost can be avoided by buying the subassemblies.
Differential Costs Per Unit
Total Differential Costs for 40,000 Units
Make Buy Make Buy
Outside supplier’s price. . $8.00 $320,00
0 Direct materials... $2.75 $110,00
0 Direct labor ($4.00 ×
0.75)... 3.00 120,000 Variable overhead
($0.60 × 0.75)... 0.45 18,000 Supervision... 0.75 30,000
Equipment rental*... 1.50 60,000 Total... $8.45 $8.00 $338,00
0 $320,00 0 Difference in favor of
buying $0.45 $18,000
* $60,000 per year ÷ 40,000 units per year = $1.50 per unit
2. a. Note that unit costs for both supervision and equipment rental will change if the company needs 50,000
subassemblies each year. These fixed costs will be spread over a larger number of units, thereby decreasing the cost per unit.
Differential Costs Per
Unit
Total Differential Costs—50,000
Units
Make Buy Make Buy
Outside supplier’s price.... $8.00 $400,00
0 Direct materials... $2.75 $137,500
Direct labor... 3.00 150,000 Variable overhead... 0.45 22,500 Supervision
($30,000 ÷ 50,000 units) 0.60 30,000 Equipment rental
($60,000 ÷ 50,000 units) 1.20 60,000 Total... $8.00 $8.00 $400,000 $400,00 0 Difference... $0 $0
The company would be indifferent between the two alternatives if 50,000 subassemblies were needed each year.
Problem 13-23 (continued)
b. Again, notice that the unit costs for both supervision and equipment rental decrease with the greater volume of units.
Differential Costs Per
Unit
Total Differential Costs—60,000
Units Mak
e Buy Make Buy
Outside supplier’s price.... $8.0
0 $480,000
Direct materials... $2.7
5 $165,00
0 Direct labor... 3.00 180,000 Variable overhead... 0.45 27,000 Supervision
($30,000 ÷ 60,000 units) 0.50 30,000 Equipment rental
($60,000 ÷ 60,000 units) 1.00 60,00
0 Total... $7.7
0 $8.0
0 $462,00
0 $480,000 Difference in favor of
making $0.3
0 $18,000
The company should rent the new equipment and make the subassemblies if 60,000 units per year are needed.
3. Other factors that the company should consider include:
a. Will volume in future years be increasing, or will it remain constant at 40,000 units per year? (If volume increases, then renting the new equipment becomes more desirable, as
shown in the computations above.)
b. Can quality control be maintained if the subassemblies are purchased from the outside supplier?
c. Does the company have some other profitable use for the space now being used to produce the subassemblies? Does production of the subassemblies require use of a constrained resource?
d. Will the outside supplier be dependable in meeting shipping schedules?
e. Can the company begin making the subassemblies again if the supplier proves to be undependable, or are there
alternative suppliers?
f. If the outside supplier’s offer is accepted and the need for subassemblies increases in future years, will the supplier have the capacity to provide more than 40,000
subassemblies per year?
g. Will the rental cost of the equipment change in the future?
Problem 13-24 (45 minutes) Direct labor cost per
unit... $ 4.80 $ 3.00 $ 8.40 $ 6.00 $ 2.40 Direct labor-hours per
unit* (a)... 0.40 0.25 0.70 0.50 0.20 Selling price... $35.00 $24.00 $22.0
0 $18.0
0 $14.00 Variable costs:
Direct materials... 3.50 2.30 4.50 3.10 1.50 Direct labor... 4.80 3.00 8.40 6.00 2.40 Variable overhead.... 1.60 1.00 2.80 2.00 0.80
* Direct labor cost per unit ÷ $12.00 per direct labor-hour 2.
Total DLHs required. . 161,900
3. Since the Cari doll has the lowest contribution margin per labor hour, its production should be reduced by 17,000 dolls (11,900
4. Since the additional capacity would be used to produce the Cari doll, the company should be willing to pay up to $21.00 per DLH ($12.00 usual labor rate plus $9.00 contribution margin per DLH) for added labor time. Thus, the company could
employ workers for overtime at the usual time-and-a-half rate of $18.00 per hour ($12.00 × 1.5 = $18.00) and still improve overall profit.
5. Additional output could be obtained in a number of ways including working overtime, adding another shift, expanding the workforce, contracting out some work to outside suppliers, and eliminating wasted labor time in the production process.
The first four methods are costly, but the last method can add capacity at very low cost.
Technical note: Some would argue that direct labor is a fixed cost in this situation and should be excluded when computing the contribution margin per unit. However, when deciding which products to emphasize, no harm is done by
misclassifying a fixed cost as a variable cost—providing that the fixed cost is the constraint. If direct labor were removed from the variable cost category, the net effect would be to bump up the contribution margin per direct labor-hour by
$12.00 for each of the products. The products will be ranked exactly the same—in terms of the contribution margin per unit of the constrained resource—whether direct labor is considered variable or fixed. However, if labor is not fixed and is not the constraint, including labor cost in the calculation of the
contribution margin may lead to incorrect rankings of the products.
Problem 13-25 (45 minutes)
1. A product should be processed further if the incremental
revenue from the further processing exceeds the incremental costs. The incremental revenue from further processing of the honey is:
Selling price of a container of honey drop
candies... $4.40 Selling price of three-quarters of a pound of
honey ($3.00 × 3/4)... 2.25 Incremental revenue per container... $2.15 The incremental variable costs are:
Decorative container... $0.40 Other ingredients... 0.25 Direct labor... 0.20 Variable manufacturing overhead... 0.10 Commissions (5% × $4.40)... 0.22 Incremental variable cost per container... $1.17 Therefore, the incremental contribution margin is $0.98 per container ($2.15 – $1.17). The cost of purchasing the
honeycombs is not relevant because those costs are incurred regardless of whether the honey is sold outright or processed further into candies.
2. The only avoidable fixed costs of the honey drop candies are the master candy maker’s salary and the fixed portion of the salesperson’s compensation. Therefore, the number of
containers of the candy that must be sold each month to justify continued processing of the honey into candies is determined as follows:
Master candy maker’s salary... $3,880 Salesperson’s fixed compensation... 2,000
If the company can sell more than 6,000 containers of the candies each month, then profits will be higher than if the honey were simply sold outright. If the company cannot sell at least 6,000 containers of the candies each month, then profits will be higher if the company discontinues making honey drop candies. To verify this, we show below the total contribution to profits of sales of 5,000, 6,000, and 7,000 containers of
candies, contrasted to sales of equivalent amounts of honey.
For example, instead of selling 4,500 pounds of honey, this same amount of honey can be processed into 6,000 containers of candy.
Sales of candies:
Containers sold per month... 5,000 6,000 7,000 Sales revenue @ $4.40 per
container... $22,00
0 $26,400 $30,800 Less incremental variable costs @
$1.17 per container... 5,850 7,020 8,190 Incremental contribution margin... 16,150 19,380 22,610 Less avoidable fixed costs... 5,880 5,880 5,880 Total contribution to profits... $10,27
0 $13,500 $16,730 Sales of equivalent amount of
honey:
Pounds sold per month*... 3,750 4,500 5,250 Sales revenue @ $3.00 per pound $11,25
0 $13,500 $15,750
* 5,000 containers × 3/4 pounds per container = 3,750 pounds
6,000 containers × 3/4 pounds per container = 4,500 pounds
7,000 containers × 3/4 pounds per container = 5,250 pounds
If there is a choice between selling 3,750 pounds of honey or selling 5,000 containers of candies, profits would be higher selling the honey outright ($11,250 versus $10,270). The
company should be indifferent between selling 4,500 pounds of honey or 6,000 containers of candy. In either case, the
contribution to profits would be $13,500. On the other hand, if faced with a choice of selling 5,250 pounds of honey or 7,000 containers of candies, profits would be higher processing the honey into candies ($16,730 versus $15,750).
1. The lowest price Jenco could bid for the one-time special order of 25,000 pounds (25 lots) without losing money would be
$34,750—the relevant cost of the order, as shown below.
Direct materials:
CW-3: 400 pounds per lot × 25 lots = 10,000 pounds.
Substitute CN-5 on a one-for-one basis to its total of 5,500 pounds. If CN-5 is not used in this order, it will be salvaged for $500. Therefore, the relevant
cost is... $ 500 The remaining 4,500 pounds would be CW-3 at a
cost of $0.90 per pound... 4,050 JX-6: 300 pounds per lot × 25 lots = 7,500 pounds at
$0.60 per pound... 4,500 MZ-8: 200 pounds per lot × 25 lots = 5,000 pounds
at $1.60 per pound... 8,000 BE-7: 100 pounds per lot × 25 lots = 2,500 pounds at
$0.55 per pound, the amount Jenco could realize by selling BE-7 [$0.65 market price – $0.10 handling
charge]... 1,37 5 Total direct materials cost... 18,42 5 Direct labor: 30 DLHs per lot × 25 lots = 750 DLHs. Because
only 400 hours can be scheduled during regular time this month, overtime would have to be used for the remaining 350 hours.
400 DLHs × $14.00 per DLH... 5,600 350 DLHs × $21.00 per DLH... 7,35 0 Total direct labor cost... 12,95 0 Overhead: This special order will not increase fixed overhead
costs. Therefore, only the variable overhead is relevant.
750 DLHs × $4.50 per DLH... 3,375 Total relevant cost of the special order... $34,75 0
Case 13-26 (continued)
2. In this part, we calculate the price for recurring orders of 25,000 pounds (25 lots) using the company’s rule of marking up its full manufacturing cost. This is probably not the best pricing policy to follow, but is a common practice in business.
Direct materials: Because of the possibility that future orders would exhaust existing inventories of CN-5 and BE-7 and new supplies would have to be purchased, all raw materials
should be charged at their expected future cost, which is the current market price.
CW-3: 10,000 pounds × $0.90 per pound... $ 9,000 JX-6: 7,500 pounds × $0.60 per pound... 4,500 MZ-8: 5,000 pounds × $1.60 per pound... 8,000 BE-7: 2,500 pounds × $0.65 per pound... 1,625 Total direct materials cost... $23,125 Direct labor: 60% (i.e., 450 DLHs) of the production of a batch
can be done on regular time; but the remaining production (i.e., 300 DLHs) must be done on overtime.
Regular time 450 DLHs × $14.00 per DLH... $ 6,300 Overtime premium 300 DLHs × $21.00 per
DLH... 6,300 Total direct labor cost... $12,600 Overhead: The full manufacturing cost includes both fixed and
variable manufacturing overhead.
Manufacturing overhead applied:
750 DLHs × $12.00 per DLH... $ 9,000 Full manufacturing cost... $44,725 Markup (40% × $44,725)... 17,890 Selling price (full manufacturing cost plus
markup)... $62,615
1. The original cost of the facilities at Ashton is a sunk cost and should be ignored in any decision. The decision being
considered here is whether to continue operations at Ashton.
The only relevant costs are the future facility costs that would be affected by this decision. If the facility were shut down, the Ashton facility has no resale value. In addition, if the Ashton facility were sold, the company would have to rent additional space at the remaining processing centers. On the other hand, if the facility were to remain in operation, the building should last indefinitely, so the company does not have to be
concerned about eventually replacing it. Essentially, there is no real cost at this point of using the Ashton facility despite what the financial performance report indicates. Indeed, it might be a better idea to consider shutting down the other facilities since the rent on those facilities might be avoided.
The costs that are relevant in the decision to shut down the Ashton facility are:
Increase in rent at Pocatello and Idaho Falls. . . $400,000 Decrease in local administrative expenses... (60,000 ) Net increase in costs... $340,000
In addition, there would be costs of moving the equipment from Ashton and there might be some loss of revenues due to
disruption of services. In sum, closing down the Ashton facility will almost certainly lead to a decline in FSC’s profits.
Even though closing down the Ashton facility would result in a decline in overall company profits, it would result in an
improved performance report for the Great Basin Region
(ignoring the costs of moving equipment and potential loss of revenues from disruption of service to customers).
Case 13-27 (continued)
Financial Performance
After Shutting Down the Ashton Facility Great Basin Region
Total Revenues... $20,000,00
0 Operating expenses:
Direct labor... 12,200,000 Variable overhead... 400,000 Equipment depreciation... 2,100,000 Facility expenses*... 1,500,000 Local administrative expenses**... 390,000 Regional administrative expenses 400,000 Corporate administrative
expenses... 1,600,000 Total operating expense... 18,590,000 Net operating income... $ 1,410,000
* $2,000,000 – $900,000 + $400,000 =
$1,500,000
** $450,000 – $60,000 = $390,000
2. If the Ashton facility is shut down, FSC’s profits will decline, employees will lose their jobs, and customers will at least
temporarily suffer some decline in service. Therefore, Braun is willing to sacrifice the interests of the company, its employees, and its customers just to make his performance report look better.
While Braun is not a management accountant, the Standards of Ethical Conduct for Management Accountants still provide
useful guidelines. By recommending closing the Ashton facility,
however, it is not fair to hold him responsible for the mistake made by his predecessor.
Case 13-27 (continued)
It should be noted that the performance report required by corporate headquarters is likely to lead to other problems such as the one illustrated here. The arbitrary allocations of
corporate and regional administrative expenses to processing centers may make other processing centers appear to be unprofitable even though they are not. In this case, the problems created by these arbitrary allocations were
compounded by using an irrelevant facilities expense figure on the performance report.
3. Prices should be set ignoring the depreciation on the Ashton facility. As argued in part (1) above, the real cost of using the Ashton facility at this point is zero. Any attempt to recover the sunk cost of the original cost of the building by charging higher prices than the market will bear will lead to less business and lower profits.
1. The product margins computed by the accounting department for the drums and mountain bike frames should not be used in the decision of which product to make. The product margins are lower than they should be due to the presence of allocated
fixed common costs that are irrelevant in this decision.
Moreover, even after the irrelevant costs have been removed, what matters is the profitability of the two products in relation to the amount of the constrained resource—welding time—that they use. A product with a very low margin may be desirable if it uses very little of the constrained resource. In short, the financial data provided by the accounting department are pretty much useless for making this decision.
2. Students may have answered this question assuming that direct labor is a variable cost, even though the case strongly hints that direct labor is a fixed cost. The solution is shown here assuming that direct labor is fixed. The solution assuming that direct labor is variable will be shown in part (4).
Solution assuming direct labor is fixed
Manufactured Selling price... $154.00 $154.00 $65.00 Variable costs:
Direct materials... 120.00 44.50 17.50 Variable manufacturing
Case 13-28 (continued)
3. Since the demand for the welding machine exceeds the 2,000 hours that are available, products that use the machine should be prioritized based on their contribution margin per welding hour. The computations are carried out below under the
assumption that direct labor is a fixed cost and then under the assumption that it is a variable cost.
Solution assuming direct labor is fixed
Manufactured XSX
Drums
Mountai n Bike Frames Contribution margin per unit (above) (a)... $107.60 $46.50 Welding hours per unit (b)... 0.8 hour 0.2 hour Contribution margin per welding hour (a)
÷ (b)... $134.50
per hour $232.50 per hour
Since the contribution margin per unit of the constrained resource (i.e., welding time) is larger for the mountain bike frames than for the XSX drums, the frames make the most profitable use of the welding machine. Consequently, the company should manufacture as many mountain bike frames as possible up to demand and then use any leftover capacity to produce XSX drums. Buying the drums from the outside supplier can fill any remaining unsatisfied demand for XSX drums. The necessary calculations are carried out below.
Analysis assuming direct labor is a fixed cost
(a) (b) (c) (a) × (c)
produced... 3,500 $ 46.50 0.20 700 1,300 $162,75 0
margin and net operating
income... 1
4. The computation of the contribution margins and the analysis of the best product mix are repeated here under the
assumption that direct labor costs are variable.
Solution assuming direct labor is a variable cost
Manufactured Selling price... $154.00 $154.00 $65.00 Variable costs:
Direct materials... 120.00 44.50 17.50 Direct labor... 0.00 4.50 22.50 Variable manufacturing Solution assuming direct labor is a variable cost
Manufactured Contribution margin per unit (above) (a)... $103.10 $24.00 Welding hours per unit (b)...
0.8 hour 0.2 hour Contribution margin per welding hour (a)
÷ (b)... $128.88
per hour $120.00 per hour When direct labor is assumed to be a variable cost, the
conclusion is reversed from the case in which direct labor is assumed to be a fixed cost—the XSX drums appear to be a
better use of the constraint than the mountain bike frames. The assumption about the behavior of direct labor really does
matter.
Case 13-28 (continued)
Solution assuming direct labor is a variable cost
(a) (b) (c) (a) × (c)
5. The case strongly suggests that direct labor is fixed: “The mountain bike frames could be produced with existing
equipment and personnel.” Nevertheless, it would be a good idea to examine how much labor time is really needed under the two opposing plans.
Some caution is advised. Plan 1 assumes that direct labor is a fixed cost. However, this plan requires over 4,000 more direct labor-hours than Plan 2 and the present situation. A full-time employee works about 1,900 hours a year, so the added
workload is about equivalent to two full-time employees. Does the plant really have that much idle time at present? If so, and if shifting workers over to making mountain bike frames would not jeopardize operations elsewhere, then Plan 1 is indeed the better plan. However, if taking on the mountain bike frame as a new product would lead to pressure to hire two more workers, more analysis is in order. It is still best to view direct labor as a fixed cost, but taking on the frames as a new product would lead to a jump in fixed costs of about $68,400 (1,900 hours ×
$18 per hour × 2). This must be covered by the additional contribution margin or the plan should be rejected. See the additional analysis on the next page.
Case 13-28 (continued)
Contribution margin from Plan 1:
Mountain bike frames produced (3,500 ×
$46.50)... $162,75 0 XSX Drums—make (1,625 × $107.60)... 174,850 XSX Drums—buy (1,375 × $33.15)... 45,58 1 Total contribution margin... 383,181 Less: Additional fixed labor costs... 68,40 0 Net effect of Plan 1 on net operating income... $314,78 1 Contribution margin from Plan 2:...
XSX Drums—make (2,500 × $107.60)... $269,00 0 XSX Drums—buy (500 × $33.15)... 16,57 5 Net effect of Plan 2 on net operating income... $285,57 5 Net advantage of Plan 1... $ 29,20 6 Plan 1, introducing the new product, would still be optimal even if two more direct labor employees would have to be hired. The reason for this is subtle. If the company does not make the XSX drums itself, it can still buy them. Thus, using an hour of
welding time to make the mountain bike frames does not mean giving up a contribution margin of $128.88 on drums (assuming direct labor is a variable cost). The opportunity cost of using the welding machine to produce mountain bike frames is less than this since a purchased drum can replace a manufactured drum. An amended analysis using the opportunity cost concept
Amended solution assuming direct labor is fixed Contribution margin per unit (above) (a)... $74.45* $46.50 Welding hours per unit (b)... 0.8 hour 0.2 hour Contribution margin per welding hour (a)
÷ (b)... $93.06
per hour $232.50 per hour Amended solution assuming direct labor is a variable
per hour $232.50 per hour Amended solution assuming direct labor is a variable